Speed-sensorless induction motor drives have developed significantly during the past few years. Speed-adaptive full-order flux observers are promising flux estimators for induction motor drives. The speed-adaptive observer consists of a state-variable observer augmented with a speed-adaptation loop. The observer gain and the speed-adaptation law determine the observer dynamics.
The conventional speed-adaptation law was originally derived using the Lyapunov stability theorem or the Popov hyperstability theorem. However, the stability of the adaptation law is not guaranteed since, controversial assumptions regarding nonmeasurable states have been used in and the positive-realness condition is not satisfied in. An unstable region encountered in the regenerating mode at low speeds is well known. The regenerating-mode low-speed operation is problematic also for the estimators based on the voltage model as shown in.
In the case of the speed-adaptive full-order flux observer, the size of the unstable region could be reduced or, in theory, even removed by choosing the observer gain suitably. However, based on the simulations carried out, the methods and are sensitive to very small errors in the motor parameters. Furthermore, a seamless transition from the regenerating-mode low-speed operation to higher-speed operation or motoring-mode operation may be problematic.
Another approach to remedy the instability is to modify the speed-adaptation law. This approach seems to be almost unexplored. In changing the direction of the error projection of the adaptation law was discussed (but not Studied) for a filtered back-emf-based observer. In the rotor flux estimate included in the adaptation law was replaced with the stator flux estimate, but this does not remove the unstable region.